Cleaning:

Dirt? Gotta take it apart. I can't think of any other way to do it.

Unless this is a high-end super-cube, you would be best off buying a new cube. The effort involved in taking apart a cube is a pain and the only good reason to do that is when you are lubricating it in the first place. If you’ve already put a significant amount of wear-and-tear on it, it was likely on its way out anyway. Also, it may be susceptible to damage from taking it apart if it’s worn.

A less expensive, yet still painstaking idea is you can try replacing the stickers (replacements are available online) because much of the yuck yuck is built up in the stickers. Once the stickers are off you can gently wipe it.

If you plan on going through a real jam session with it, you might want to wash your hands thoroughly first and a few times along the way. This will get the additional oils off of your fingers that can create some of the grime on it.

Lubrication:

If this is a Rubik's-branded cube there is only so much you can do to make it spin faster. I've found that some Rubik's-branded cubes turned very well out of the box; and others turned like crap. So the problem goes deeper than just with the lubrication, they have poor quality control. From what I've heard it depends what particular manufacturing facility they are made in.

Everyone recommends silicone, but that is designed for speedcubing and in most cases speedcubers aren’t even using a Rubik’s-branded cube. There are other manufacturers that make a better cube and most speedcubers prefer to build their own using DIY (Do-it-yourself) kits. There are also pre-assembled speedcubes but they of course cost significantly more.

So if you are interested in speedcubing, get a different cube at www.cube4you.com or www.puzl.co.uk. If you want to make things just a little easier, use Vaseline by twisting the top layer 45 degrees and removing the edge piece. Rub a reasonable amount of Vaseline on this side and then (with the piece still missing) spin it 180 degrees to do the other side. This will avoid the need to pop out 2 edge pieces. Flip it over and repeat the process on the opposite/bottom layer. Then rotate it 90 degrees and do the same process one more time.

Some people will highly recommend against Vaseline but it works just fine for beginners/intermediate users.